Determinable Solutions for One-dimensional Quantum Potentials: Scattering, Quasi-bound and Bound State Problems

摘要

We derive analytic expressions of the recursive solutions to theSchr\"{o}dinger's equation by means of a cutoff potential technique forone-dimensional piecewise constant potentials. These solutions provide a methodfor accurately determining the transmission probabilities as well as the wavefunction in both classically accessible region and inaccessible region for anybarrier potentials. It is also shown that the energy eigenvalues and the wavefunctions of bound states can be obtained for potential-well structures byexploiting this method. Calculational results of illustrative examples areshown in order to verify this method for treating barrier and potential-wellproblems.